US Patent publication 20030209221 (the '221 publication, published Nov. 13, 2003) discloses a two-dimensional rotary displacement device comprises a housing, an outer rotor and at least one inner rotor. The axes of rotation of the outer rotor and the at least one inner rotor are parallel. The inner rotor rotates within the outer rotor as the outer rotor rotates within the housing. International patent publication no. WO07/019703 published Feb. 22, 2007 (the '703 publication) discloses a two-dimensional rotary displacement device comprising a stator with an internal rotor that spins on a shaft on a rotating carrier. As the carrier rotates within the stator, the inner rotor spins around the shaft and meshes with the stator. Each of these devices uses an inner rotor. There is described below an improvement on the inner rotor disclosed in the '221 publication and the '703 publication.